kinematics 1d kinematics 2d dynamics work and energy

Kinematics 1D

Kinematics 2D

Dynamics

Work and Energy

Kinematics – 1 Dimension

All about motion problems

Frame of Reference – orientation of an object’s motion

Used to anchor coordinate axes

For many problems, you can choose the orientation of your coordinate axes (down is positive and up is negative, if you like)

Be logical though! Don’t try to complicate the problem more than it is already.



Some vocab

Scalar

Vector

Distance

Displacement

Average speed

Average velocity

Instantaneous velocity

Acceleration

Average acceleration

Instantaneous acceleration


Motion at Constant Acceleration

Use your Kinematic Friends!

Most, if not all, kinematic problems are constant acceleration problems

Falling Objects

Uniform acceleration of 9.81 m/s2

The sign of g depends on your frame of reference


PT Graphs

Slope = velocity

+ slope = + velocity

- slope = - velocity

0 slope = 0 velocity

VT Graphs Slope = acceleration + slope = + accel.

- slope = - accel.

0 slope = 0 accel.

Curve sloping toward x-axis = slowing down

Curve sloping away from x-axis = speeding up


Multiple Choice Questions – TIMED!

Quietly answer the questions on your own.

Multiple Choice Answers

1. D

2. D

3. A

4. E

5. B

6. C

7. D

8. A

9. E

10. B

Kinematics – 2 Dimensions

Vector Addition – Graphical Method Head – to – Tail Method Place the head of the first vector at the tail of the second

vector

Repeat for successive vectors

For the resultant vector, draw an arrow from where you started to where you ended (from tail of first vector to head of second vector).

Use ruler to measure length (magnitude)

Use protractor to measure direction w.r.t. a reference axis


Vector Addition – Mathematics Method

Adding by components

Breaking a vector down into components is called vector resolution

Add x-components together to get Rx

Add y-components together to get Ry

Pythagorean theorem, sqrt(Rx2 + Ry

2)

tan-1 = (opp. component/adj. component)


Vector Addition

To subtract a vector, flip the direction by 180˚

Multiplying a vector V by a scalar, c, produces a vector with magnitude cV in the direction of V.


Projectile Motion Vertical component of motion is independent of

horizontal motion Horizontal component is constant (vix = vfx and ax = 0)

Vertical component changes with g

How to solve Treat motions separately!

Write displacement, velocity and acceleration in terms of x- and y-components. USE KINEMATIC FRIENDS!

Use t-chart method or some other strategy to organize data


Projectile Motion, con’t

The only data common to both motions is the time of flight (t) and the angle of launch (θ)

Often you will need to solve a systems of equations

Because time and the angle are constant to both motions, solve one equation for time or angle and substitute


Relative Motion

Problems are simply vector addition problems


Kinematic – 2 Dimensions




1. D

2. C

3. E

4. B

5. C

6. A

7. C

8. E

9. D

10. B

Dynamics: Motion and Force

Force is a push or pull between two objects

Vector! Magnitude and direction

Newton’s First Law of Motion (Law of Inertia)

An object in motion will stay in motion, and an object at rest will stay at rest, unless acted upon by an unbalanced force

Inertia – ability of an object to maintain motion (resistance to change in motion)

Depends on mass of object (more mass = more inertia)

Dynamics

Mass is the measure of ‘amount of stuff’ – measured

in kilograms

Weight is the measure of ‘the force of gravity on that stuff’ – measured in Newtons

Newton’s Second Law of Motion

∑F = ma

Balanced forces, ∑F = 0

Unbalanced forces result in an acceleration of the object

Dynamics

How to solve problems

Draw a FBD!

Summation of forces

∑F = max

∑F = may

Apply Kinematic Friends as needed

Dynamics

Newton’s Third Law of Motion

For every action there is an equal and opposite reaction

Forces come in pairs – there must be two objects for forces to exist

Dynamics

Other Forces

Normal force – force due to the contact between an object and a surface

Frictional force – force between two surfaces sliding (kinetic), or trying to slide (static), across each other – dependent on normal force

Spring/Elastic force – restoring force due to a spring or other elastic object

Tension – force due to rope, string, cord, wire, etc.

Dynamics

Dynamics




1. B

2. D

3. A

4. D

5. C

6. E

7. B

8. D

9. D

10. C

Work and Energy

Work Done By a Constant Force

W = Fdcosθ

θ is the angle btn force and displacement

Work is measured in Joules

The perpendicular component of the force does no work

Work done by friction is always negative since it opposes motion

Work and Energy

Work Done By a Varying Force

Use a force-displacement graph

Find the area under the curve

Work and Energy

Conservation of Energy

Energy cannot be created nor destroyed

Kinetic Energy KE = ½ mv2

Energy due to an object’s motion – has the capacity to do work

Work-Energy Theorem

The work done on an object will result in a change in its kinetic energy and, subsequently, a negative change in its potential energy W = ΔKE and W = -ΔPE

Work and Energy

Potential Energy

Due to its position with regard to other bodies

Gravitational potential

Refers to capacity of an object to do work based on the force of gravity acting on it

PEg = mgh, h is determined by your zero level

Spring/Elastic potential

A spring stretched or compressed has the capacity to do work once that displacing force is removed

PEs = ½ kx2

Work and Energy

Conservative Forces

Forces for which the work done is independent of the path taken

Work depends only on starting and finishing positions

Examples: gravity, spring/elastic, etc.

Non-Conservative Forces

Work done depends on path taken

Example: friction

WNC = ΔKE + ΔPE

Work and Energy

Power

Rate at which work is done

OR

Rate at which energy is transformed

P = W/t OR P=E/t

Measured in Watts, W

Work and Energy

Work and Energy




1. E

2. D

3. B

4. E

5. D

6. E

7. C

8. B

9. A

10. E

kinematics 1d kinematics 2d dynamics work and energy

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